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Single-Voice Transformations: A Model for Parsimonious Voice Leading
Author: Brandon Derfler
Date Of Publication: Mar 2010
Isbn13: 978-1-4438-1860-5
Isbn: 1-4438-1860-7
This study demonstrates how smooth voice leading in music can be effectively modeled using concepts from abstract algebra. Minute voice-leading displacements are explained as iterations of the basic operation, the single-semitone transformation (SST). The SST is a type of transformation in which only a single voice in a chord is transposed by a semitone. Unlike previous music theoretic studies, the SST model does not rely on twelve-tone operations on sets to determine voice-leading paths. SST-succession classes can then be defined; they allow SSTs to be generalized as parsimonious voice-leading relations between pair-ordered set classes. Voice leading between chords of different “sizes” can be obtained through split and fuse operations. Once a mathematical basis for smooth voice-leading is formalized, 3D graphical representations in the form of lattices of parsimoniously related chord types can be developed. The study compares the single-voice transformational model to transformational theories of atonal voice leading and to recent work in the emergent field of neo-Riemannian theory. The final chapter examines music from tonal, atonal, and “post-atonal” stylistic periods by Chopin, Scriabin, Webern, Paul Lansky, and John Adams, showing the new voice-leading model’s versatility as an analytical tool.
Brandon Derfler holds an MA degree in Musicology from the University of North Carolina at Chapel Hill and a PhD in Music Theory from the University of Washington. His publications have appeared in GAMUT, Indiana Theory Review, and Perspectives of New Music. He is Associate Provost at the Academy of Music Northwest.
“Brandon Derfler's Single-Voice Transformations: A Model for Parsimonious Voice Leading explores neo-Riemannian and parsimonious voice-leading relations among generalized types of set classes. It summarizes very clearly the bewildering variety of terminology and ideas in this area, and goes on to develop an approach based on n-tuples of pitch-classes for chords, related to one another by “single-semitone transformations” (the parsimonious aspect here) assembled into a direct product group that acts on the chord-tuples. This is a mathematical treatment that is more correct and superior to previous approaches. The thesis includes some very impressive online 3-dimensional virtual reality fly-through models of the geometry of chord types under these relations.
A must-read for anyone interested in this area of music theory research.” —John Rahn, Professor of Music, University of Washington, Editor, Perspectives of New Music
Price Uk Gbp: 39.99
Price Us Usd: 59.99
Sample pdf (including Table of Contents)
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From Navigating Music and Sound Education
“We rarely have the opportunity and time to engage with the practicalities of music teaching through the lens of evidence-based practice. This book provides us with a wonderful exception that is accessible to beginning and established teachers. It contains a wide range of stimulating and thought-provoking material that draws on real-world experiences and events, which are contextualised, informed and structured by theory. This is a powerful combination that we can visit again and again for insight and inspiration. Congratulations to all involved, particularly the editors for shaping such a valuable contribution!”
—Professor Graham F. Welch, University of London; President, International Society of Music Education
“Navigating music and sound education draws together a range of issues increasingly acknowledged to be at the basis of reflective and effective music learning and teaching: social settings, cultural dimensions, gender, indigeneity, varying cognitive approaches, inter-disciplinary connections, technology, types of learning, and creativity. It opens up areas of pedagogy that go beyond classroom methodology to acknowledge student individuality and encourage music learning and teaching grounded in the reality of students’ musical and social lives. It will be invaluable for those training to become educators and for teachers already in the field.”
—Associate Professor Peter Dunbar-Hall, University of Sydney
“This book brings an important contribution to music teacher education as it challenges the readers to rethink their paradigms of music education. It highlights the importance of preparing a reflective teacher, autonomous, creative and conscious of the multifaceted and multicultural locus in which they will work. The book also draws on the importance for music teachers to consider the context in which they work, and establish a dialog between local musical traditions, informal music practices and global trends of music teaching and learning. Most importantly, all chapters are in one way or another derived from research carried out on specific areas, thus stressing the importance of the research informed practice in music education.”
—Professor Liane Hentschke, Federal University of Rio Grande do Sul, Brazil; International Society of Music Education Immediate Past President
Many readers will appreciate Steve Dillon and Kathy Hirche’s description of the future of education in their work with dynamic technological contexts.
Navigating Music and Sound Education is a wonderful guide and resource for pre-service music teachers, for teachers in the field, and for teacher educators.
It offers a range of fresh perspectives on the state of music education as it is and as it might be. Kari K Veblen
Navigating Music and Sound Education is an ambitious project which features current research from 20 individuals whose professional identities run the gamut from musician to songwriter to student to educator to music therapist to ethnomusicologist. The book’s scope is perhaps the most exciting aspect of Navigating Music and Sound Education.
Kari K Veblen
University of Western Ontario
British Journal of Music Education
October 2011
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